On the mechanical modeling of cell components. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Klinge, Sandra; Wiegold, Tillmann; Aygün, Serhat; Gilbert, Robert P.; Holzapfel, Gerhard A.
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000129
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Eukaryotic cells are complex systems which carry out a variety of different tasks. The current contribution gives insight into the modeling of some of their vital components and represents an overview of results achieved within the international D‐A‐CH project on computational modeling of transport processes in a cell. The first part of the contribution studies viscoelastic effects of cross‐linked actin network embedded in cytosol. The basic‐model is used to simulate the actin behavior at a microscopic level. It considers the influence of the physical length, the end‐to‐end distance and the stretch modulus in order to provide a relationship between the stretch of a single polymer chain and the applied tension force. The effective behavior of the cell cytoplasm is simulated by using the multiscale finite element method. Here, a standard large strain viscous approach is applied for the cytosol, while the generalized Maxwell model simulates viscous effects occurring in filaments due to deviatoric changes. The examples dealing with combinations of tension‐holding tests give insight into the effective behavior of the cytoplasm. The second part of the talk deals with the viral entry into a cell driven by the receptor motion. In the model developed, the receptor motion is described by the diffusion equation along with two boundary conditions. The first condition represents the balance of fluxes at the front of the contact area. To this end, the velocity is assumed to be proportional to the gradient of the chemical potential. The second condition deals with the energy balance and postulates that the difference in the energy behind and before the front causes the front's movement. The important energy contributions are energy due to the binding of receptors, the free energy of the membrane, the bending energy and the kinetic energy due to the motion of the receptors. The model yields a well‐posed moving boundary problem, which is numerically solved using the finite difference method. The change of receptor density over the membrane as well as the motion of the front of the adhesion zone is studied in the numerical simulations.